Likewise, the problem of computing a quantity on a manifold which is invariant under differentiable mappings is inherently global, since any local invariant will be trivial in the sense that it is already exhibited in the topology of R < sup > n </ sup >.

Likewise, a functor from G to the category of vector spaces, Vect < sub > K </ sub >, is a linear representation of G. In general, a functor G → C can be considered as an " action " of G on an object in the category C. If C is a group, then this action is a group homomorphism.

Likewise, the number for " K " in Europe can refer to the weight of an equivalent quantity of K < sub > 2 </ sub > O, whereas in Australia it refers to elemental potassium.

Likewise if we assume five-character upper case keys, there are K = 26 < sup > 5 </ sup > possible keys, of which the majority will not " work ".

Likewise, < tt > TH </ tt >, < tt > ER </ tt >, < tt > ON </ tt >, and < tt > AN </ tt > are the most common pairs of letters ( termed bigrams or digraphs ), and < tt > SS </ tt >, < tt > EE </ tt >, < tt > TT </ tt >, and < tt > FF </ tt > are the most common repeats.

Likewise, the model space for a pseudo-Riemannian manifold of signature (< var > p </ var >, < var > q </ var >) is </ sup > with the metric

Likewise the representations of this Hopf algebra turn out to be Z < sub > 2 </ sub >- graded comodules.

Likewise, all non-linear operations performed on discrete-time signals must be bandlimited to F < sub > s </ sub >/ 2-ε. Wagner's book Analytical Transients proves why equality is not permissible.

Likewise, S < sup > 2n + 1 </ sup > is a principal U ( 1 )- bundle over complex projective space CP < sup > n </ sup > and S < sup > 4n + 3 </ sup > is a principal Sp ( 1 )- bundle over quaternionic projective space HP < sup > n </ sup >.

* Likewise, Old Dutch ( from Proto-Germanic ) becomes a centralising diphthong, spelled < oe > or < ou >.

Likewise, the two dimensional Hausdorff measure of a measurable subset of R < sup > 2 </ sup > is proportional to the area of the set.

** Likewise, the distance from F < sub > 2 </ sub > to P is the same as the distance from P < sub > 2 </ sub > to P, because lines PF < sub > 2 </ sub > and PP < sub > 2 </ sub > are both tangent to the same sphere ( G2 ).

Likewise, for any given total body CO < sub > 2 </ sub > production rate, alveolar ventilation is inversely proportional to end-tidal CO < sub > 2 </ sub > concentration ( since their mutual product must equal total body CO < sub > 2 </ sub > production rate ).

Likewise, a project slogan is to " break down the bars of ignorance and illiteracy ", because its volunteers aim to continue spreading public literacy and appreciation for the literary heritage just as public libraries began to do in the late 19th century .< ref >

Likewise using the 4 × 4 Dirac gamma matrices gives rise to the 4 component Dirac spinors used in 3 + 1 dimensional relativistic quantum field theory.

Likewise, the integers 2 and 3 are not composite numbers because each of them can only be divided by one and itself.

Likewise, 1 hour is equal to 60 minutes, or 3, 600 seconds.

Likewise, Gary Taylor in his analysis of the authorship of 1 Henry VI, argues that the many discrepancies between 1 Henry VI and 2 Henry VI ( such as the lack of reference to Talbot ) coupled with similarities in the vocabulary, phraseology and tropes of 1 Henry VI and 3 Henry VI suggest 1 Henry VI was probably written last.

Likewise, Charles Barkley was one of the most dominating power forwards, despite also reaching only 6 feet 4 3 / 4 inches ( 1. 95 mt ).

Likewise, the Double Eagle was specifically created as such by name (" An Act to authorize the Coinage of Gold Dollars and Double Eagles ", title and section 1, March 3, 1849 ).

Likewise, the 3-liter cars ( e. g., ' E300 ') where also re-badged to ' E320 ' with the new 3. 2 litre engines and naming rationalization of 1994.

Likewise, the bsTan -' gyur contains 3, 387 texts using 127, 000 folios amounting to 850, 000 lines and 48 millions words.

Likewise, the composers ' second fugues ( A minor for Shostakovich, C minor for Bach ) utilize very similar opening rhythms for their fugue subjects ( two 16th notes followed by 3 eighth notes, twice in a row ).

Likewise, despite heavy casualties in one of the Australian companies and battalion headquarters 3 RAR had emerged from the intense battle largely intact and had successfully withdrawn in an orderly fashion.

Likewise, if we turn over the red card and find that it has the label " 3 ", this also does not break the rule.

Likewise, the powertrains were also as fitted to the Toyota with a twin-cam, EFI 2. 2 litre 5S-FE straight-four producing and, with an optional quad-cam EFI 3. 0 litre 3VZ-FE V6 making and.

Likewise, a CPVI score of D + 3 shows that a generic Democratic candidate would be expected to receive 3 percentage points more votes than the national average.

Likewise, it is the best for the decision-maker to move from scenario 3 to scenario 1.

Likewise the China Yangtze Patrol gunboats also became part of the Philippine naval defenses: ( sunk south of Java 3 March 1942 ), ( lost 2 May 1942 ), ( scuttled 6 May 1942 but salvaged by the Japanese ), ( sunk 5 May 1942 ), and ( scuttled 5 May 1942 ).

An increase of 20 percent from the base period in the Finished Goods Price Index, for example, is shown as 120. 0, which can be expressed in dollars as follows: “ Prices received by domestic producers of a systematic sample of finished goods have risen from $ 100 in 1982 to $ 120 today .” Likewise, a current index of 133. 3 would indicate that prices received by producers of finished goods today are one-third higher than what they were in 1982.

Likewise, Sega's Streets of Rage 3 removed a gay villain wearing Village People attire and transformed a transsexual villain into a man with long hair.

Likewise with attempted aggravated arson, recklessness towards loss of life will suffice ( A-G's Reference # 3 1992 ).

Likewise, Level II is providing water for 47. 39 % of all households, while Level III only served 3. 62 % of the total.

Likewise, IGN gave the game 7. 3, reporting the same problems ; the enemy being too easy to defeat, A. I.

Likewise, a set of trailing points on the western side allows ' Up ' trains on the Up Main track to terminate on platform 3 and return towards the west on the ' Down Main ' track.

Likewise, commonly ' measured ' anions include chloride ( Cl < sup >−</ sup >), bicarbonate ( HCO < sub > 3 </ sub >< sup >−</ sup >) and phosphate ( H < sub > 2 </ sub > PO < sub > 4 </ sub >< sup >−</ sup >), while commonly ' unmeasured ' anions include sulfates and a number of serum proteins.

Likewise, a group of atoms can remain bound to each other, forming a molecule.

Likewise, there is a formula for combining the covariances of two sets that can be used to parallelize the computation:

Likewise, a baserunner can attempt to steal a base, or the batter can choose to swing at an intentional ball ; however, these rarely occur since taking these risks is rarely more beneficial to the offensive team than allowing the walk.

Likewise, bony fish can release the ammonia into the water where it is quickly diluted.

Likewise, the angular momentum can be measured from far away using frame dragging by the gravitomagnetic field.

Likewise, if a substance can form crystals, it can also form polycrystals.

Likewise, spheres are compact, but a sphere missing a point is not since a sequence of points can tend to the missing point without tending to any point within the space.

Likewise, the menstrual cycle in women with epilepsy can influence patterns of seizure recurrence.

Likewise, graph theory is useful in biology and conservation efforts where a vertex can represent regions where certain species exist ( or habitats ) and the edges represent migration paths, or movement between the regions.

Likewise, grappling sports have been devised so that their participants can compete using full physical effort without injuring their opponents.

Likewise, the tradename Hycodan points to its relationship with oxycodone ( Percodan ) hy-for hydrogen, per-for oxygen ( as in potassium permanganate ) -- this can also be seen with other trade names for other drugs, like Permonid ( desomorphine ) and Hydal ( hydromorphone ).

Likewise, a below favorable oxygen content can make life just as difficult.

Likewise, one can construe semantic internalism in two ways, as a denial of either of these two theses.

Likewise, every use of modus ponens can be converted to a use of modus tollens and transposition.

Likewise, a player with can use his 5-5 to play the full house.

Likewise, it can never have zero energy, meaning that the particle can never " sit still ".

Likewise, these components that aid in insertion of the photo, referred to as slip agents, can break down and transfer from the plastic to the photograph, where they deposit as an oily film, attracting further lint and dust.

Likewise, if Q ( x, n ) denotes the number of n-free integers ( e. g. 3-free integers being cube-free integers ) between 1 and x, one can show

Likewise, two sets of one-sided tetrominos can be fit to a rectangle in more than one way.

Likewise, catalase has one of the highest turnover numbers of all enzymes ; one catalase molecule can convert millions of molecules of hydrogen peroxide to water and oxygen each second.